
SIGMA 2 (2006), 021, 10 pages condmat/0602427
https://doi.org/10.3842/SIGMA.2006.021
On the Degenerate Multiplicity of the sl_{2} Loop Algebra for the 6V Transfer Matrix at Roots of Unity
Tetsuo Deguchi
Department of Physics, Faculty of Science, Ochanomizu University, 211 Ohtsuka, BunkyoKu, Tokyo 1128610, Japan
Received October 31, 2005, in final form February 06, 2006; Published online February 17, 2006
Abstract
We review the main result of condmat/0503564. The
Hamiltonian of the XXZ spin chain and the transfer matrix of the
sixvertex model has the sl_{2} loop algebra symmetry if the q
parameter is given by a root of unity, q_{0}^{2N} = 1, for an
integer N. We discuss the dimensions of the degenerate
eigenspace generated by a regular Bethe state in some sectors,
rigorously as follows:
We show that every regular Bethe ansatz eigenvector in the sectors is
a highest weight vector and derive the highest weight
d_{k}^{±},
which leads to evaluation parameters a_{j}.
If the evaluation parameters are distinct, we obtain the
dimensions of the highest weight representation generated by the
regular Bethe state.
Key words:
loop algebra; the sixvertex model; roots of unity representations of quantum groups; Drinfeld polynomial.
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